线性预测的自相关算法

线性预测中的自相关系数

1．原理

线性预测是语音编码中的基本算法，其基本原理如下： 设语音信号的样值序列Xk Xk x1,x2, ,xk ，第k时刻的取样值xk可以用之前的P个样值的线性组合来预测。

k aixk i x

i 1P

实际样值与预测值之间的误差为：

k xk aixk i ek xk x

i 1P

因此预测系统的传递函数为：

H Z X Z

EZ 1

1 aiz i

i 1P 1 AZ其中H(Z)是一个全极点滤波器，称为综合滤波器。A(Z)是H(Z)的逆滤波器，称为分析滤波器。在语音线性预测编码中，A(Z)的系数反映了声道特性。

为了使预测误差最小，采用最小均方误差准则，即使误差的均方值

2 k E ek E xk x2

k

k 1 2 P

E xk aixk i k 1 i 1 PP2

最小。在预测阶数P给定后， k2就是所有预测系数 ai 的函数，因此：

2 ek x k k 0 E 2 xk x ai ai

k xk i 0 E xk x

可见，要使ek的预测误差最小，则ek必须与所有数据xk i正交，称为正

交性原理。将上式展开，可得：

E xkxk i ajE xk jxk i

j 1P

其中E xk jxk i R k j,k i ，即信号的自相关系数。对平稳信号（语音信号一般不是平稳信号，但对单独处理的每帧来说，可以近似认为是短时平稳信号）来说，

R k i,k j R i j

R i R i

因此，可以得到：

R 1 R P 1 a1 R 1 R 0 R2R1R2 RP 2 a2 RPRP 1RP 2 R0 aP

解此线性方程组，即可得到各预测系数。一般采用Levison-Durbin算法递推求解。在已知输入信号的情况下，必须先求各阶自相关系数。

2．G.729中的线性预测

ITU-T G.729语音编码标准采用CS-ACELP混合编码方法，输出码率为8kbps，每帧语音长度10ms，在8kHz采样条件下，具有80个样点。在线性预测时一般采用连续3帧进行加窗处理后进行，因此计算

自相关系数的数组具有240个样点值。

下面是G.729参考代码中的相关程序部分，并附加说明。 void Autocorr(

Word16 x[], /* (i) : Input signal */

Word16 m, /* (i) : LPC order */

Word16 r_h[], /* (o) : Autocorrelations (msb) */

Word16 r_l[] /* (o) : Autocorrelations (lsb) */

)

{

Word16 i, j, norm;

Word16 y[L_WINDOW];

Word32 sum;

extern Flag Overflow;

/* Windowing of signal */

for(i=0; i<L_WINDOW; i++)

{

y[i] = mult_r(x[i], hamwindow[i]);

}

/* Compute r[0] and test for overflow */

do {

Overflow = 0;

sum = 1; /* Avoid case of all zeros */

for(i=0; i<L_WINDOW; i++)

sum = L_mac(sum, y[i], y[i]);

/* If overflow divide y[] by 4 */

if(Overflow != 0)

{

for(i=0; i<L_WINDOW; i++)

{

y[i] = shr(y[i], 2);

}

}

}while (Overflow != 0);

/* Normalization of r[0] */

norm = norm_l(sum);

sum = L_shl(sum, norm);

L_Extract(sum, &r_h[0], &r_l[0]); /* Put in DPF format (see oper_32b) */

/* r[1] to r[m] */

for (i = 1; i <= m; i++)

{

sum = 0;

for(j=0; j<L_WINDOW-i; j++)

sum = L_mac(sum, y[j], y[j+i]);

sum = L_shl(sum, norm);

L_Extract(sum, &r_h[i], &r_l[i]);

}

return;

}

/*___________________________________________________________________________ | | | Function Name : mult_r | | | | Purpose : | | | | Same as mult with rounding, i.e.: | | mult_r(var1,var2) = shr(((var1*var2) + 16384),15) and |

| mult_r(-32768,-32768) = 32767. | | | | Complexity weight : 2 | | | | Inputs : | | | | var1 | | 16 bit short signed integer (Word16) whose value falls in the |

| range : 0xffff 8000 <= var1 <= 0x0000 7fff. |

| | | var2 | | 16 bit short signed integer (Word16) whose value falls in the |

| range : 0xffff 8000 <= var1 <= 0x0000 7fff. |

| | | Outputs : | | | | none | | | | Return Value : | | | | var_out |

| 16 bit short signed integer (Word16) whose value falls in the |

| range : 0xffff 8000 <= var_out <= 0x0000 7fff. |

|___________________________________________________________________________| */

Word16 mult_r(Word16 var1, Word16 var2)

{

Word16 var_out;

Word32 L_produit_arr;

L_produit_arr = (Word32)var1 * (Word32)var2; /* product */

L_produit_arr += (Word32) 0x00004000; /* round */

L_produit_arr &= (Word32) 0xffff8000L;

L_produit_arr >>= 15; /* shift */

if (L_produit_arr & (Word32) 0x00010000L) /* sign extend when necessary */ {

L_produit_arr |= (Word32) 0xffff0000L;

}

var_out = sature(L_produit_arr);

return(var_out);

}

/*___________________________________________________________________________ | | | Function Name : norm_l | | | | Purpose : | | | | Produces the number of left shift needed to normalize the 32 bit varia- |

| ble l_var1 for positive values on the interval with minimum of |

| 1073741824 and maximum of 2147483647, and for negative values on the in-|

| terval with minimum of -2147483648 and maximum of -1073741824; in order |

| to normalize the result, the following operation must be done : |

| norm_L_var1 = L_shl(L_var1,norm_l(L_var1)). |

| | | Complexity weight : 30 | | | | Inputs : | | | | L_var1 | | 32 bit long signed integer (Word32) whose value falls in the |

| range : 0x8000 0000 <= var1 <= 0x7fff ffff. |

| |

| | | none | | | | Return Value : | | | | var_out | | 16 bit short signed integer (Word16) whose value falls in the |

| range : 0x0000 0000 <= var_out <= 0x0000 001f. |

|___________________________________________________________________________| */

Word16 norm_l(Word32 L_var1)

{

Word16 var_out;

if (L_var1 == 0)

{

var_out = 0;

}

else

{

if (L_var1 == (Word32)0xffffffffL)

{

var_out = 31;

}

else

{

if (L_var1 < 0)

{

L_var1 = ~L_var1;

}

for(var_out = 0;L_var1 < (Word32)0x40000000L;var_out++)

{

L_var1 <<= 1;

}

}

}

return(var_out);

}

/*___________________________________________________________________________

| Function Name : L_mac | | | | Purpose : | | | | Multiply var1 by var2 and shift the result left by 1. Add the 32 bit |

| result to L_var3 with saturation, return a 32 bit result: |

| L_mac(L_var3,var1,var2) = L_add(L_var3,(L_mult(var1,var2)). |

| | | Complexity weight : 1 | | | | Inputs : | | | | L_var3 32 bit long signed integer (Word32) whose value falls in the |

| range : 0x8000 0000 <= L_var3 <= 0x7fff ffff. |

| | | var1 | | 16 bit short signed integer (Word16) whose value falls in the |

| range : 0xffff 8000 <= var1 <= 0x0000 7fff. |

| | | var2 | | 16 bit short signed integer (Word16) whose value falls in the |

| range : 0xffff 8000 <= var1 <= 0x0000 7fff. |

| | | Outputs : | | | | none | | | | Return Value : | | | | L_var_out | | 32 bit long signed integer (Word32) whose value falls in the |

| range : 0x8000 0000 <= L_var_out <= 0x7fff ffff. |

|___________________________________________________________________________| */

Word32 L_mac(Word32 L_var3, Word16 var1, Word16 var2)

{

Word32 L_var_out;

Word32 L_produit;

L_produit = L_mult(var1,var2);

L_var_out = L_add(L_var3,L_produit);

return(L_var_out);

}

/* Hamming_cos window for LPC analysis. */

/* Create with function ham_cos(window,200,40) */

Word16 hamwindow[L_WINDOW] = {

2621, 2623, 2629, 2638, 2651, 2668, 2689, 2713, 2741, 2772,

2808, 2847, 2890, 2936, 2986, 3040, 3097, 3158, 3223, 3291,

3363, 3438, 3517, 3599, 3685, 3774, 3867, 3963, 4063, 4166,

4272, 4382, 4495, 4611, 4731, 4853, 4979, 5108, 5240, 5376,

5514, 5655, 5800, 5947, 6097, 6250, 6406, 6565, 6726, 6890,

7057, 7227, 7399, 7573, 7750, 7930, 8112, 8296, 8483, 8672,

8863, 9057, 9252, 9450, 9650, 9852, 10055, 10261, 10468, 10677,

10888, 11101, 11315, 11531, 11748, 11967, 12187, 12409, 12632, 12856,

13082, 13308, 13536, 13764, 13994, 14225, 14456, 14688, 14921, 15155,

15389, 15624, 15859, 16095, 16331, 16568, 16805, 17042, 17279, 17516,

17754, 17991, 18228, 18465, 18702, 18939, 19175, 19411, 19647, 19882,

20117, 20350, 20584, 20816, 21048, 21279, 21509, 21738, 21967, 22194,

22420, 22644, 22868, 23090, 23311, 23531, 23749, 23965, 24181, 24394,

24606, 24816, 25024, 25231, 25435, 25638, 25839, 26037, 26234, 26428,

26621, 26811, 26999, 27184, 27368, 27548, 27727, 27903, 28076, 28247,

28415, 28581, 28743, 28903, 29061, 29215, 29367, 29515, 29661, 29804,

29944, 30081, 30214, 30345, 30472, 30597, 30718, 30836, 30950, 31062,

31170, 31274, 31376, 31474, 31568, 31659, 31747, 31831, 31911, 31988,

32062, 32132, 32198, 32261, 32320, 32376, 32428, 32476, 32521, 32561,

32599, 32632, 32662, 32688, 32711, 32729, 32744, 32755, 32763, 32767,

32767, 32741, 32665, 32537, 32359, 32129, 31850, 31521, 31143, 30716,

30242, 29720, 29151, 28538, 27879, 27177, 26433, 25647, 24821, 23957,

23055, 22117, 21145, 20139, 19102, 18036, 16941, 15820, 14674, 13505,

12315, 11106, 9879, 8637, 7381, 6114, 4838, 3554, 2264, 971};

3．设计要求

利用TMS320C54x汇编实现自相关函数的计算。使用附带的输入测试数据，并与附带的输出测试数据比较，验证结果的正确性。

1． 需要优化代码，利用专门的汇编指令完成相应的运算。

2． 对于L_mac函数可以使用mac指令实现。

3． 对于Mult_r可以使用MPYR指令。

4． 对于溢出检查可以等计算完成后进行。

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